Recall that the Adams-Hilton model (cf. [1]}), over any field \(\mathbb {K}\) , of a simply connected finite type CW-complex \(X\)  is a chain algebra morphism \(\begin{tikzcd} \theta _X :(TV,d)[r,"\simeq "] & C_{\ast }(\Omega X) \end{tikzcd}\)  such that \(H_{\ast }(\theta _X)\)  is an isomorphism of graded algebras with \(V\)  such that \(H_{i-1}(V,d_1)\cong H_i(X;\mathbb {K})\)  and \(d_1: V\rightarrow V\)  is the linear part of \(d\) .
